For most programming jobs experience in the the tech stack is the defining factor, as most programming jobs do not require deep domain expertise (whatever the domain is: computing, business, etc).
Of course general problem solving ability is still valuable but it is more difficult to assess than a candidate´s experience in some tech stack.
So, for the general programming market the tech stack is the defining factor. The only way you can navigate between jobs with different tech stacks is by having an insider that guarantees the hiring manager that you have what it takes to learn the new tech stack without trouble, or by finding some company which is desperate enough to take the risk.
Of course general problem solving ability is still valuable but it is more difficult to assess than a candidate´s experience in some tech stack.
So, for the general programming market the tech stack is the defining factor. The only way you can navigate between jobs with different tech stacks is by having an insider that guarantees the hiring manager that you have what it takes to learn the new tech stack without trouble, or by finding some company which is desperate enough to take the risk.
You can label yourself what you want.